1. Parameters

In this script, we share the code to replicate our parameters.

0. File architecture

Create architecture for scripts, visuals and data. Includes sensitivity_analysis_lq

I. Load data

II. Demand

## `geom_smooth()` using formula = 'y ~ x'

## Saving 7 x 5 in image
## `geom_smooth()` using formula = 'y ~ x'
## 
## Call:
## lm(formula = price_ton_toto ~ c, data = new_dat)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -669851 -246794  -50249  201334 1366925 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1625837     406790   3.997 0.000248 ***
## c              -1564        726  -2.154 0.036890 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 431700 on 43 degrees of freedom
## Multiple R-squared:  0.09739,    Adjusted R-squared:  0.0764 
## F-statistic:  4.64 on 1 and 43 DF,  p-value: 0.03689

II. Biological parameters

##      [,1]           [,2]         
## [1,] "K"            "M"          
## [2,] "Winfinity"    "Loo"        
## [3,] "tmax"         "tm"         
## [4,] "Lm"           "Temperature"
## [5,] "ln_margsd"    "rho"        
## [6,] "logitbound_h" "ln_r"
## Closest match: Actinopterygii_Perciformes_Sciaenidae_Totoaba_macdonaldi
x
Loo 4.9184344
K -1.5830689
Winfinity 10.0590626
tmax 2.7171232
tm 1.3175891
M -1.0570853
Lm 4.1868676
Temperature 24.0087354
ln_var -2.7136658
rho 0.6039179
ln_MASPS -0.1039645
ln_margsd -1.0414289
h 0.5263985
logitbound_h -0.5141059
ln_Fmsy_over_M -0.0887666
ln_Fmsy -1.1601266
ln_r -1.9234144
r 0.2012827
ln_G 2.1021294
G 8.3517745

III. Poaching costs

A. Build total cost function

1. Build average subseasonal costs

First :

  • Use w_parto reconstruct costs of crew earning, food, fuel, gear

  • Compute a cost per trip, with confiscations of gear and vessels

  • Compute sub-seasonal average costs

2. Total cost from seasonal average cost

We have average cost data, for bins of trips. Here, I estimate a cost function for all the effort levels, that maps the number of trips to their total cost, taking into account different bins.

## [1]    0   40  520 1920

## [1] 14386.69

The kinky total cost function could be best approximated with a linear term. However, to model the increasing opportunity costs of having more fishermen, it would be nice to have a quadratic term, to forecast the future.

B. Estimate \(W, W_1, W_2\)

1. Estimate \(W\)

Find the parameter \(W_{quad}\) such that : \[ TotCost(E)=WE^2 \Rightarrow MargCost(E) = 2W_{quad}E \]

And

\[ MargCost(E_{hist}) = AvgCost(E_{hist})\Rightarrow W_{quad} = \frac{W_{avg}}{2E_{hist}} \]

2. Estimate \(W_1, W_2\)

First, find best estimate of modeled cost in a MMSE sense.

## [1] "Optimal W1 in an MMSE sense is : 0"
## [1] "Optimal W2 in an MMSE sense is : 7193.34486399167"

Result from MMSE suggest to use the linear form, without reference to a quadratic term. However, increasing cost of effort is consistent with a disaggregated view of the fishery. Force a quadratic term.

W1 W2 diff% mse
0 0.0000000 0.0000000 0
11000 0.8819504 11.7702188 30647515448353752
11400 0.7777838 10.3800450 24033220500031512
11800 0.6736171 8.9898711 18274620332517136
12200 0.5694504 7.5996973 13371714945810632
12600 0.4652838 6.2095234 9324504339911994
13000 0.3611171 4.8193495 6132988514821220
13400 0.2569504 3.4291757 3797167470538315
13800 0.1527838 2.0390018 2317041207063276
14200 0.0486171 0.6488279 1692609724396104

Here, I keep as the baseline specification the first value with low difference with cost

3. Export data and sources for W

Export data for \(W\) and the corresponding model parameters for the quadratic model (\(W\)) and linear-quadratic model (\(W_1\) and \(W_2\))

IV. Trading costs

We use c= 0 as trading costs.

V. Farming costs

At 4.5 years under farming conditions, a totoaba should have a 416.96g swim bladder. At 5 years under farming conditions, a totoaba should have a 529.78 g swim bladder

Quasi-fixed cost for set-up

The quasi fixed cost for pens is cost_pen from the Buche Bros data

VI. Save calibration data

params value concept units
alpha 1625836.98 Demand model : intercept USD
beta 1563.75 Demand model : coefficient USD/metric ton of biomass
r 0.20 Intrinsic growth rate unitless
k 20226.00 Carrying capacity (in metric tons) metric tons of biomass
sigma 0.00 Catchability % of biomass/vessel trip
avg_cost 14386.69 Average cost per vessel trip at historical value USD/vessel trip
W_high 3.75 Quadratic cost parameter - Quadratic cost function USD vessel trip\(^{-2}\)
fixed_cost 13811222.14 Fixed cost - Quadratic cost function USD
W1 12200.00 Linear cost parameter - Linear quadratic cost function USD/vessel trip
W2 0.57 Quadratic cost parameter - Linear quadratic cost function USD vessel trip\(^{-2}\)
age 4.50 Age of farmed totoaba Years
gamma 1354.25 Demand model : substitutable good coefficient USD/metric ton of biomass
v 89929.92 Unit cost of farming USD/metric ton of biomass
i_r 0.10 Interest rate %
c 0.00 Unit cost of trading USD/ metric ton of biomass
cost_pen 200000.00 Cost of pen USD

2. Model baseline

I. Load data

In this section, I load data for the baseline calibration using the linear and linear quadratic cost models.

params value concept units
alpha 1625836.98 Demand model : intercept USD
beta 1563.75 Demand model : coefficient USD/metric ton of biomass
r 0.20 Intrinsic growth rate unitless
k 20226.00 Carrying capacity (in metric tons) metric tons of biomass
sigma 0.00 Catchability % of biomass/vessel trip
avg_cost 14386.69 Average cost per vessel trip at historical value USD/vessel trip
W_high 3.75 Quadratic cost parameter - Quadratic cost function USD vessel trip\(^{-2}\)
fixed_cost 13811222.14 Fixed cost - Quadratic cost function USD
W1 12200.00 Linear cost parameter - Linear quadratic cost function USD/vessel trip
W2 0.57 Quadratic cost parameter - Linear quadratic cost function USD vessel trip\(^{-2}\)
age 4.50 Age of farmed totoaba Years
gamma 1354.25 Demand model : substitutable good coefficient USD/metric ton of biomass
v 89929.92 Unit cost of farming USD/metric ton of biomass
i_r 0.10 Interest rate %
c 0.00 Unit cost of trading USD/ metric ton of biomass
cost_pen 200000.00 Cost of pen USD

II. Define functions

Define function where variable is either x i.e population stock, or s i.e price paid to poachers. All the parameters take default values specified in the global environment.

  • growth(x, ...) : logistic growth function, yields growth of population (in metric tons)

  • monop_harvest(x, ...): harvest (in metric tons) when trader is a monopolist

  • monop_harvest_lq(x, ...): harvest (in metric tons) when trader is a monopolist and cost structure is linear quadratic

  • cournot_harvest(x, ...), bertrand_harvest(x, ...): harvest (in metric tons) when trader and farmer compete in Cournot, i.e, set quantities strategically, and Bertrand, i.e, set prices strategically.

  • cournot_harvest_lq(x, ...) : harvest (in metric tons) when trader and farmer compete in Cournot i.e, set quantities strategically and cost structure is linear quadratic

  • price_poachers_cournot(x, ...), price_poachers_bertrand(x, ...): price paid to poachers (in USD/metric tons) when trader and farmer compete in Cournot and Bertrand

  • price_poachers_bertrand(x, ...): price paid to poachers (in USD/metric tons) when trader and farmer compete in Bertrand and cost structure is linear quadratic

  • bertrand_harvest_lq(x,...) is set replacing the price that clears the primary market in the harvest function of fishermen.

  • cournot_farmed(s, ...), bertrand_farmed(s, ...): quantity farmed (in metric tons) when trader and farmer compete in Cournot and Bertrand

III. Generate results

Generate results saved at ~/data/outputs/results_all_models.csv :

  • Set cost variables using W_lq_new: each row corresponds to a cost parameter \(W\), \(W_1\) and \(W_2\)

Graph outputs :

A. Understanding the impact of different values of W1 and W2

To understand the impact of different \(W_1\) & \(W_2\) divides :

Clearly, the choice of \(W_1\) and \(W_2\) is important with respect to the anticipated equilibrium in the vertical monopoly case : with a linear-quadratic cost function, we no longer can say the monopoly will achieve a healthy steady state population. The results in the post intervention world are robust to the cost specification, and guarantee population increases in the quantity adjustment scenario, while population may marginally diminish in the price setting scenario.

B. Graph with prefered specification

First, illustrate the new equilibria with the same \(W\) = 3.7465338 value and the prefered solution for \(W_1\) and \(W_2\) (e.g 12200, 0.57) in the linear quadratic cost of effort specification.

Save plot for final results :

Define bio-economic performance by combining population variables (stock and harvest) with price and profit data from economic model.

Change in number of totoabas :

tinytable_9ufxg7ad17wpkcnsze58
Bioeconomic performance - with baseline specification
Scenario Poached harvest (in mt) Farmed harvest (in mt) Steady state population (in mt) Retail price (in USD/ton of buche) Retail price of 500g buche (in USD) Price paid to poacher (in USD/ton of buche) Poacher price of 500g buche (in USD) Illegal profit (in million USD) Farming profit (in million USD) Fishing profit (in million USD) Aggregate profit (in million USD) Aggregate profit change (in million USD) Farming profit change (in million USD) Illegal profit change (in million USD) Fishing profit change (in million USD) Variation in ss. pop. Poaching change (%)
Price setting - LQ cost 536.70 430.05 17235.0 204179.1 5247.402 39870.05 1024.6602 88.18 58.14 3.57 149.89 -253.35 58.14 -313.84 2.34 -0.24% 5.85%
Vertical Monopoly - LQ cost 507.04 0.00 17277.0 832955.7 21406.962 40074.46 1029.9136 402.02 0.00 1.22 403.24 0.00 0.00 0.00 0.00 0% 0%
Quantity adjustment - LQ cost 363.71 333.60 18220.5 605295.6 15556.098 36537.13 939.0044 206.87 173.43 0.57 380.86 -22.38 173.43 -195.16 -0.66 5.46% -28.27%
Price setting 520.27 425.30 17184.0 236298.3 6072.866 32903.89 845.6299 105.82 70.11 8.56 184.49 -229.80 70.11 -300.33 0.42 -0.43% 2.09%
Vertical Monopoly 509.64 0.00 17259.0 828894.3 21302.583 31951.60 821.1560 406.15 0.00 8.14 414.29 0.00 0.00 0.00 0.00 0% 0%
Quantity adjustment 369.87 330.94 18182.0 599279.2 15401.476 20894.42 536.9866 213.93 170.66 3.86 388.45 -25.84 170.66 -192.22 -4.28 5.35% -27.42%

New version for manuscript :

tinytable_q67egg3o3xr38jadgeso
Scenario Poached harvest (in mt & % change) Farmed harvest (in mt) Steady state population (in mt & % change) Trader profit (in million USD and change) Fishing profit (in million USD and change) Farming profit
Linear quadratic cost
Vertical Monopoly 507.04 0 17277 402.02 1.22 0
0% 0% 0 0
Quantity adjustment 363.71 333.6 18220.5 206.87 0.57 173.43
-28.27% 5.46% -195.16 -0.66
Price setting 536.7 430.05 17235 88.18 3.57 58.14
5.85% -0.24% -313.84 2.34
Quadratic cost
Vertical Monopoly 509.64 0 17259 406.15 8.14 0
0% 0% 0 0
Quantity adjustment 369.87 330.94 18182 213.93 3.86 170.66
-27.42% 5.35% -192.22 -4.28
Price setting 520.27 425.3 17184 105.82 8.56 70.11
2.09% -0.43% -300.33 0.42

Table for manuscript :

tinytable_gc30nidoiubp7xm6y7mn
Bioeconomic performance
Scenario Poached harvest (in mt) Farmed harvest (in mt) Steady state population (in mt) Illegal profit (in million USD) Farming profit (in million USD) Fishing profit (in million USD) Aggregate profit (in million USD) Illegal profit change (in million USD) Variation in ss. pop. Poaching change (%)
Vertical Monopoly 507.04 0.00 17277.0 402.02 0.00 1.22 403.24 0.00 0% 0%
Quantity adjustment 363.71 333.60 18220.5 206.87 173.43 0.57 380.86 -195.16 5.46% -28.27%
Price setting 536.70 430.05 17235.0 88.18 58.14 3.57 149.89 -313.84 -0.24% 5.85%

3. Sensitivity analysis

Sensitivity analysis

A. Load data

B. Set up parameter space

Redo parameter for sensitivity analysis :

C. Run model

Define model run, and yield exploit_ a dataset with parameters and corresponding steady states.

Check the occurrence of steady states :

D. Analysis

1. Impact of variation of cost parameters in fishermen profit

## Saving 7 x 5 in image
names x x_norm multiplier_global
Price setting 17235.0 -0.2430978 0 %
Vertical monopoly 17277.0 0.0000000 0 %
Quantity adjustment 18220.5 5.4610175 0 %
Vertical monopoly 1361.0 -92.1224750 -10 %
Vertical monopoly 1598.0 -90.7507090 -10 %
Vertical monopoly 17267.5 -0.0549864 -10 %
Price setting 17205.5 -0.4138450 -10 %
Quantity adjustment 18210.0 5.4002431 -10 %
Price setting 17261.5 -0.0897146 10 %
Vertical monopoly 17286.0 0.0520924 10 %
Quantity adjustment 18229.0 5.5102159 10 %
Price setting 17289.5 0.0723505 20 %
Vertical monopoly 17295.0 0.1041848 20 %
Quantity adjustment 18238.5 5.5652023 20 %
Vertical monopoly 17304.5 0.1591712 30 %
Price setting 17317.0 0.2315217 30 %
Quantity adjustment 18248.0 5.6201887 30 %

Need a subsidy rate of 20% to avoid poaching increase, eg need \(v=\) 71943.9322629

## Saving 7 x 5 in image
names x x_norm namer
Price setting 17229.5 -0.2749320 11000 and 0.88
Vertical monopoly 17275.5 -0.0086821 11000 and 0.88
Quantity adjustment 18216.5 5.4378654 11000 and 0.88
Price setting 17231.5 -0.2633559 11400 and 0.78
Vertical monopoly 17276.0 -0.0057880 11400 and 0.78
Quantity adjustment 18218.0 5.4465474 11400 and 0.78
Price setting 17233.0 -0.2546738 11800 and 0.67
Vertical monopoly 17276.5 -0.0028940 11800 and 0.67
Quantity adjustment 18219.0 5.4523355 11800 and 0.67
Price setting 17235.0 -0.2430978 12200 and 0.57
Vertical monopoly 17277.0 0.0000000 12200 and 0.57
Quantity adjustment 18220.5 5.4610175 12200 and 0.57
Vertical monopoly 1106.5 -93.5955316 12600 and 0.47
Vertical monopoly 1842.5 -89.3355328 12600 and 0.47
Vertical monopoly 17278.0 0.0057880 12600 and 0.47
Price setting 17236.5 -0.2344157 12600 and 0.47
Quantity adjustment 18221.5 5.4668056 12600 and 0.47
Vertical monopoly 934.0 -94.5939689 13000 and 0.36
Vertical monopoly 2014.5 -88.3399896 13000 and 0.36
Vertical monopoly 17278.5 0.0086821 13000 and 0.36
Price setting 17238.5 -0.2228396 13000 and 0.36
Quantity adjustment 18223.0 5.4754876 13000 and 0.36
Vertical monopoly 804.5 -95.3435203 13400 and 0.26
Vertical monopoly 2143.5 -87.5933322 13400 and 0.26
Vertical monopoly 17279.0 0.0115761 13400 and 0.26
Price setting 17240.5 -0.2112635 13400 and 0.26
Quantity adjustment 18224.0 5.4812757 13400 and 0.26
Vertical monopoly 696.0 -95.9715228 13800 and 0.15
Vertical monopoly 2251.0 -86.9711177 13800 and 0.15
Vertical monopoly 17279.5 0.0144701 13800 and 0.15
Price setting 17242.0 -0.2025815 13800 and 0.15
Quantity adjustment 18225.5 5.4899577 13800 and 0.15
Vertical monopoly 601.0 -96.5213868 14200 and 0.05
Vertical monopoly 2345.5 -86.4241477 14200 and 0.05
Vertical monopoly 17280.5 0.0202581 14200 and 0.05
Price setting 17244.0 -0.1910054 14200 and 0.05
Quantity adjustment 18226.5 5.4957458 14200 and 0.05
Price setting 17251.0 -0.1504891 12100 and 0.88
Vertical monopoly 17282.5 0.0318342 12100 and 0.88
Quantity adjustment 18224.0 5.4812757 12100 and 0.88
Price setting 17253.5 -0.1360190 12540 and 0.78
Vertical monopoly 17283.5 0.0376223 12540 and 0.78
Quantity adjustment 18225.5 5.4899577 12540 and 0.78
Price setting 17256.0 -0.1215489 12980 and 0.67
Vertical monopoly 17284.0 0.0405163 12980 and 0.67
Quantity adjustment 18227.0 5.4986398 12980 and 0.67
Price setting 17258.5 -0.1070788 13420 and 0.57
Vertical monopoly 17285.0 0.0463043 13420 and 0.57
Quantity adjustment 18228.5 5.5073219 13420 and 0.57
Vertical monopoly 1384.0 -91.9893500 13860 and 0.47
Vertical monopoly 1557.0 -90.9880188 13860 and 0.47
Vertical monopoly 17286.0 0.0520924 13860 and 0.47
Price setting 17261.5 -0.0897146 13860 and 0.47
Quantity adjustment 18230.0 5.5160039 13860 and 0.47
Vertical monopoly 1070.5 -93.8039011 14300 and 0.36
Vertical monopoly 1869.5 -89.1792557 14300 and 0.36
Vertical monopoly 17287.0 0.0578804 14300 and 0.36
Price setting 17264.0 -0.0752445 14300 and 0.36
Quantity adjustment 18231.5 5.5246860 14300 and 0.36
Vertical monopoly 911.0 -94.7270938 14740 and 0.26
Vertical monopoly 2028.0 -88.2618510 14740 and 0.26
Vertical monopoly 17287.5 0.0607744 14740 and 0.26
Price setting 17266.5 -0.0607744 14740 and 0.26
Quantity adjustment 18233.0 5.5333681 14740 and 0.26
Vertical monopoly 788.0 -95.4390230 15180 and 0.15
Vertical monopoly 2150.5 -87.5528159 15180 and 0.15
Vertical monopoly 17288.5 0.0665625 15180 and 0.15
Price setting 17269.0 -0.0463043 15180 and 0.15
Quantity adjustment 18234.5 5.5420501 15180 and 0.15
Vertical monopoly 683.5 -96.0438734 15620 and 0.05
Vertical monopoly 2254.0 -86.9537535 15620 and 0.05
Vertical monopoly 17289.5 0.0723505 15620 and 0.05
Price setting 17272.0 -0.0289402 15620 and 0.05
Quantity adjustment 18236.0 5.5507322 15620 and 0.05

2. Effect of v

## Saving 7 x 5 in image
## # A tibble: 3 × 24
##       X identifier names      names_2      x values lag_sign Stable  beta  alpha
##   <int>      <int> <chr>      <chr>    <dbl>  <dbl>    <int> <chr>  <dbl>  <dbl>
## 1   555        145 Price set… ss_ber… 17310. 0.0653        2 Stable 1564. 1.63e6
## 2   558        146 Price set… ss_ber… 17294. 0.0192        2 Stable 1564. 1.63e6
## 3   560        147 Price set… ss_ber… 17277  0.0513        2 Stable 1564. 1.63e6
## # ℹ 14 more variables: gamma <dbl>, W <dbl>, W1 <dbl>, W2 <dbl>, c <int>,
## #   v <dbl>, r <dbl>, k <int>, interest_rate <dbl>, sigma <dbl>, spec <chr>,
## #   transformation <dbl>, id_2 <int>, x_norm <dbl>

3. Impact of different v and c

4. Impact of different substitutability

5. Impact of joint variation of demand parameters

## # A tibble: 6 × 6
##   identifier names                    x alpha gamma3 Stable  
##        <int> <chr>                <dbl> <fct> <fct>  <chr>   
## 1       1869 Quantity adjustment   763  1.8   50%    Stable  
## 2       1869 Quantity adjustment  3578. 1.8   50%    Unstable
## 3       1869 Quantity adjustment 15886. 1.8   50%    Stable  
## 4       1869 Price setting         909  1.8   50%    Stable  
## 5       1869 Price setting        4996. 1.8   50%    Unstable
## 6       1869 Price setting       14322. 1.8   50%    Stable

4. Additional graphs

Figure (SM):

## Saving 7 x 5 in image

Figure (SM) and 1 in Main : Hypothetical schematic of equilibrium points under different poaching harvest functions

## Figure (SM) and 1 in Main : Alternative with extinction - Hypothetical schematic of equilibrium points under different poaching harvest functions

Figure : Different equilibria

Figure : Bertrand v. Monopoly following Damania and Bulte

Figure : Comparison between monopoly and Bertrand behavior on monopolistic and duopolistic markets following Damania and Bulte

Figure : F (x) and v summarise when Bertrand harvest is larger or lower than in monopoly

Figure : v for poaching to stop in a Bertrand equilibrium

Figure : Price per ton of totoaba and catch from 2014 to 2017

Extended data figure : Von Bertlaffery Growth curves

5. Model extensions

I. Oligopoly extension

A. Define functions

Define :

  • q_(x, N, M, ...) : Cournot harvest with N traders and M farmers (in metric tons)

  • cournot_harvest(x, ...) : Cournot harvest with 1 trader and 1 farmer (in metric tons)

  • monop_harvest(x, ...): Monopoly harvest (in metric tons)

  • growth(x, ...) : logistic growth function, yields growth of population (in metric tons)

B. Set data for analysis

i. No competition, just traders

## # A tibble: 15 × 2
##        x names      
##    <int> <chr>      
##  1   884 ss_5players
##  2   968 ss_2players
##  3   969 ss_2players
##  4  3264 ss_2players
##  5  3265 ss_2players
##  6  4974 ss_5players
##  7  4975 ss_5players
##  8 14366 ss_5players
##  9 14367 ss_5players
## 10 14368 ss_5players
## 11 15993 ss_2players
## 12 17234 ss_price   
## 13 17235 ss_price   
## 14 17277 ss_monop   
## 15 17680 ss_quantity
##   Market configuration Low stable steady state Middle unstable steady state
## 1            5 players                     884                         4975
## 2            2 players                     969                         3265
## 3    Vertical monopoly                    <NA>                         <NA>
## 4        Price setting                    <NA>                         <NA>
## 5  Quantity adjustment                    <NA>                         <NA>
##   High stable steady state
## 1                    14366
## 2                    15993
## 3                    17277
## 4                    17235
## 5                    17680

ii. Multiple traders and farmers

C. Graphical output

II. Extended cartel model

In this section, we investigate the effect of a ‘vertical monopoly’ take over the aquaculture facility. See supplementary materials section ??? for derivation and discussions.

A. Define harvest

B. Run scenario

C. Graphical output

Identify values :

##   Monopoly Takeover_ Cournot_
## 1    17277  6.572322 5.458124

Finally, identify bioeconomic performance :

tinytable_47f3ln2z5af97slesqks
Bioeconomic performance of takeover scenario
Scenario Harvest in (mt) Stock in (mt) Price paid to poachers (USD/mt) Profit in 10^6 USD
Vertical Monopoly 507.0368 17277.0 40074.45 402.0208
Cournot Competition 363.7271 18220.0 36538.33 206.8650
Cartel takeover 332.2972 18412.5 35861.28 419.9162

III. Simultaneous effects of transaction cost change and effect of competition

First, we calibrate a hypothetical cost of transaction based on most recent observed price data. Assume that the cost of transaction is 100% of the observed price paid to poachers in most recent data.

A. Find guestimate for the transaction costs

The observed price per kilogram of totoaba in most recent years is 483.0116732 USD. The model is expressed in metric tons, so we use the metric ton numbers instead to parameterize an idea of the worst case trading costs.

B. Run analysis

i. Graphical output

## [1] 289807

ii. Bioeconomic performances

Need to evaluate economic performance

##      [,1]                                               [,2]          
## [1,] "Structure"                                        "Steady state"
## [2,] "Profit of monopoly with large costs (in million)" "17895"       
## [3,] "Profit of quantity setting (in million)"          "18220"       
## [4,] "Profit of price setting (in million)"             "17234.5"     
##      [,3]             [,4]       [,5]             [,6]    
## [1,] "Variation in %" "Poaching" "Variation in %" "Profit"
## [2,] " "              "415.12"   " "              "189.51"
## [3,] "1.82"           "363.73"   "-12.38"         "206.87"
## [4,] "-3.69"          "513.08"   "23.6"           "87.71"
##   ss_monop_large ss_monop_low ss_bertrand_val ss_cournot
## 1          17895        17277         17234.5      18220
##   ss_bertrand_share_large ss_cournot_share_large poaching_monop_large
## 1               -3.690975                1.81615             415.1169
##   poaching_bertrand poaching_cournot poaching_cournot_rel poaching_bertrand_rel
## 1          513.0788         363.7271            -12.37958              23.59865

C. Check the effect of policy intervention using various values of substitutability